$ O = 80 H^{1.5} $

import pandas as pd
from sympy.solvers import solve
from sympy import Symbol
import plotly.graph_objs as go
import plotly.express as px
import numpy as np
from math import *

surf = 3000 #m^2
''' if delta y = 1 m so delta surf = 200 m^2 '''
L = 2500 #m
n = 0.013
S0 = 0.009
K1 = K2 = 0.4 #voroodi khorooji
K3 = 0.15
maxH = 5 #m
# D(tunnel) = ?
g = 9.81 # m^2/s 

Time = [3*i for i in range(17)]
Q_in = [0, 22, 48, 80, 100, 110, 113, 112, 106, 95, 83, 72, 65, 60, 57, 55, 53]
inputs = pd.DataFrame({'zaman': Time, "debi voroodi(m^3/s)": Q_in})
inputs = inputs.transpose()
inputs

See Full Dataframe in Mito

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
zaman	0	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48
debi voroodi(m^3/s)	0	22	48	80	100	110	113	112	106	95	83	72	65	60	57	55	53

heads = [0.1 * i for i in range(int(maxH/0.1 + 1))]
Os = [80 * i**1.5 for i in heads]
Vs = [10**6 * (3*i + (0.1 * i**2)) for i in heads]
VperdeltaT = [i / 10800 for i in Vs] # 3Hrs
Ns = [VperdeltaT[i] + (Os[i]/2) for i in range(len(VperdeltaT))]
df1 = pd.DataFrame({"H":heads, "O": Os, "V": Vs,
                    "V/dt": VperdeltaT, "N": Ns})
df1

See Full Dataframe in Mito

	H	O	V	V/dt	N
0	0.0	0.000000	0.0	0.000000	0.000000
1	0.1	2.529822	301000.0	27.870370	29.135281
2	0.2	7.155418	604000.0	55.925926	59.503635
3	0.3	13.145341	909000.0	84.166667	90.739337
4	0.4	20.238577	1216000.0	112.592593	122.711881
5	0.5	28.284271	1525000.0	141.203704	155.345839
6	0.6	37.180640	1836000.0	170.000000	188.590320
7	0.7	46.852961	2149000.0	198.981481	222.407962
8	0.8	57.243340	2464000.0	228.148148	256.769818
9	0.9	68.305197	2781000.0	257.500000	291.652599
10	1.0	80.000000	3100000.0	287.037037	327.037037
11	1.1	92.295179	3421000.0	316.759259	362.906849
12	1.2	105.162731	3744000.0	346.666667	399.248032
13	1.3	118.578244	4069000.0	376.759259	436.048381
14	1.4	132.520187	4396000.0	407.037037	473.297131
15	1.5	146.969385	4725000.0	437.500000	510.984692
16	1.6	161.908616	5056000.0	468.148148	549.102456
17	1.7	177.322305	5389000.0	498.981481	587.642634
18	1.8	193.196273	5724000.0	530.000000	626.598137
19	1.9	209.517541	6061000.0	561.203704	665.962474
20	2.0	226.274170	6400000.0	592.592593	705.729678
21	2.1	243.455129	6741000.0	624.166667	745.894231
22	2.2	261.050187	7084000.0	655.925926	786.451019
23	2.3	279.049816	7429000.0	687.870370	827.395279
24	2.4	297.445121	7776000.0	720.000000	868.722560
25	2.5	316.227766	8125000.0	752.314815	910.428698
26	2.6	335.389922	8476000.0	784.814815	952.509776
27	2.7	354.924217	8829000.0	817.500000	994.962109
28	2.8	374.823692	9184000.0	850.370370	1037.782216
29	2.9	395.081764	9541000.0	883.425926	1080.966808
30	3.0	415.692194	9900000.0	916.666667	1124.512764
31	3.1	436.649058	10261000.0	950.092593	1168.417122
32	3.2	457.946722	10624000.0	983.703704	1212.677065
33	3.3	479.579816	10989000.0	1017.500000	1257.289908
34	3.4	501.543218	11356000.0	1051.481481	1302.253091
35	3.5	523.832034	11725000.0	1085.648148	1347.564165
36	3.6	546.441580	12096000.0	1120.000000	1393.220790
37	3.7	569.367368	12469000.0	1154.537037	1439.220721
38	3.8	592.605096	12844000.0	1189.259259	1485.561807
39	3.9	616.150631	13221000.0	1224.166667	1532.241982
40	4.0	640.000000	13600000.0	1259.259259	1579.259259
41	4.1	664.149381	13981000.0	1294.537037	1626.611727
42	4.2	688.595091	14364000.0	1330.000000	1674.297546
43	4.3	713.333583	14749000.0	1365.648148	1722.314939
44	4.4	738.361429	15136000.0	1401.481481	1770.662196
45	4.5	763.675324	15525000.0	1437.500000	1819.337662
46	4.6	789.272070	15916000.0	1473.703704	1868.339739
47	4.7	815.148575	16309000.0	1510.092593	1917.666880
48	4.8	841.301848	16704000.0	1546.666667	1967.317591
49	4.9	867.728990	17101000.0	1583.425926	2017.290421
50	5.0	894.427191	17500000.0	1620.370370	2067.583966

fig = go.Figure()
fig.add_trace(go.Scatter(x = df1.N, y = df1.O))

x = np.array(df1.N)
y = np.array(df1.O)
m, b = np.polyfit(x, y, 1)
m, b

(0.4439886133372627, -63.18103398350222)

#mx^2 + bx 
O = lambda N: m * N + b

meanI = []
for i in range(len(Q_in)):
    try:
        I1 = Q_in[i]
        I2 = Q_in[i+1]
        meanI.append((I2 + I1) / 2)
    except:
        pass
#----------------------------------------------------------------
O0 = Q_in[0]
N1 = N0 = O0 / 2
out = [O0]
Nfinal = []
dN = meanI[0] - O0
#----------------------------------------------------------------

for i in range(len(meanI)):
    Ibar = meanI[i]
    dN = Ibar - O0
    N1 = N1 + dN
    O0 = O(N1)
    out.append(O0)

px.scatter(out)

WARNING: maghadir Debi manfi shode ast !!!

khate az marhale balatar fit mikonim: (bala boodan adad b(-63.18) mojeb in etefagh shode ast!)

ta daraje 5 manfi mishod, ba 6 emtehan mikonim:

# ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g
x = np.array(df1.N)
y = np.array(df1.O)
a, b, c, d, e, f, g = np.polyfit(x, y, 6)
O = lambda N: (a * (N**6)) + (b * N**5) + c * N**4 + d * N**3 + e * N**2 + f * N + g

O0 = Q_in[0]
N1 = N0 = O0 / 2
out = [O0]
Nfinal = []
dN = meanI[0] - O0
#----------------------------------------------------------------

for i in range(len(meanI)):
    Ibar = meanI[i]
    dN = Ibar - O0
    N1 = N1 + dN
    O0 = O(N1)
    out.append(O0)

px.scatter(out)

final = pd.DataFrame({"debi khorooji" : out, 'debi voroodi': Q_in})
final

See Full Dataframe in Mito

	debi khorooji	debi voroodi
0	0.000000	0
1	0.235429	22
2	5.427695	48
3	16.619508	80
4	34.291746	100
5	54.428756	110
6	72.478220	113
7	85.935663	112
8	93.954934	106
9	96.263270	95
10	93.702495	83
11	88.053800	72
12	81.359281	65
13	75.036937	60
14	69.608147	57
15	65.225696	55
16	61.670751	53

fig = go.Figure()
fig.add_trace(go.Scatter(x = Time, y = Q_in, name = 'Q_in'))
fig.add_trace(go.Scatter(x = Time, y = out, name = 'Q_out'))
fig.update_layout(
    title="Hydrograph",
    xaxis_title="zaman(s)",
    yaxis_title="debi(m^3/s)",
    legend_title="jaryan",
    font=dict(
        family="Courier New, monospace",
        size=18,
        color="RebeccaPurple"
    )
)

Q_max = max(out)
Q_design = 1.3 * Q_max
# Q = V A #m^3/s ===> A = Q / V 
# A = (pi* D^2) / 4 #m^2
# assumed V = 5 - 15 m/s
soratha = [v for v in range(1, 16)]
ghotrha = []
for V in soratha:
    A = Q_design / V
    D = sqrt((4*A) / pi)
    ghotrha.append(D)

fig = go.Figure()
fig.add_trace(go.Scatter(x = soratha, y = ghotrha))
fig.update_layout(
    title="نمودار قطرها برحسب سرعت های مختلف جریان",
    xaxis_title="Speed of flow (m/s)",
    yaxis_title="Diameter (m)",
    font=dict(
        size=18,
        color="Darkred"
    )
)

معادله انرژی

import IPython.display as ID
img = ID.Image("diameter.jpeg")
ID.display(img)

zarib_d = L *( (4 * n * Q_max * (4**(2/3))) / (pi) ) ** 2

$hf = \frac{40300.907138}{d^{16/3}}$

yek = maxH + L * S0
K_total = K1 + K2 + K3
do = K_total *( (((Q_max * 4) ** 2) / (2 * g * (pi**2))) )
yek , do 

(27.5, -6164.006291559182)

$ 27.5 = \frac{d}{2} + \frac{40300.907138}{d^{16/3}} + \frac{727.387872}{d^4}$

solved_d = ID.Image('solved_d.png')
ID.display(solved_d)

d = 4.06334
print('ghotre ba in ravesh barabare %f'%d)

ghotre ba in ravesh barabare 4.063340